Subgroups — D₁₁×D₃₂ #13070912

Order 1408.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₁₁×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622157	C₂	1	2	yes	maximal, complemented
4	D₃₅₂	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₁₁	—	2	2	no	—
7	C₁₁×D₁₆	C₂²	1	2	yes	complemented
8	#66890	—	2	2	no	—
9	D₁₇₆	C₂²	1	2	yes	complemented
10	C₁₆×D₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×C₃₂	C₂²	1	1	yes	characteristic, complemented
12	C₁₁⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₁₁	—	4	2	no	—
14	C₁₁×D₈	—	2	2	no	—
15	#4323	—	4	2	no	—
16	D₈₈	—	2	2	no	—
17	C₈×D₁₁	D₄	1	1	yes	characteristic
18	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
19	C₁₁⋊C₁₆	D₄	1	1	yes	characteristic
20	C₂×D₃₂	—	11	1	no	maximal, Sylow
21	C₂²×D₁₁	—	8	2	no	—
22	D₄×C₁₁	—	4	2	no	—
23	C₂²⋊D₁₁	—	8	2	no	—
24	D₄₄	—	4	2	no	—
25	C₄×D₁₁	D₈	1	1	yes	characteristic
26	C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
27	C₁₁⋊C₈	D₈	1	1	yes	characteristic
28	C₂×D₁₆	—	11	2	no	—
29	D₃₂	—	11	2	no	—
30	D₃₂	—	11	1	no	—
31	D₃₂	D₁₁	1	1	yes	characteristic, direct product factor
32	C₂×C₃₂	—	11	1	no	—
33	C₂²×C₁₁	—	8	2	no	—
34	C₂×D₁₁	—	8	2	no	—
35	C₂×D₁₁	—	16	4	no	—
36	C₂×D₁₁	D₁₆	1	1	yes	characteristic
37	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
38	Dic₁₁	D₁₆	1	1	yes	characteristic
39	C₂×D₈	—	22	2	no	—
40	D₁₆	—	11	2	no	—
41	D₁₆	—	22	2	no	—
42	D₁₆	C₂×D₁₁	1	2	yes	complemented
43	C₂×C₁₆	—	11	1	no	—
44	C₃₂	—	11	1	no	—
45	C₃₂	C₂×D₁₁	1	1	yes	characteristic, complemented
46	C₂×C₁₁	—	16	2	no	—
47	C₂×C₁₁	C₂×D₁₆	1	1	yes	characteristic
48	D₁₁	—	16	2	no	—
49	D₁₁	D₃₂	1	2	yes	direct product factor
50	C₂×D₄	—	44	2	no	—
51	D₈	—	2	2	no	—
52	D₈	—	22	2	no	—
53	D₈	—	44	2	no	—
54	C₂×C₈	—	11	1	no	—
55	C₁₆	—	11	1	no	—
56	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
57	C₁₁	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	88	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	44	2	no	—
61	D₄	—	88	2	no	—
62	C₂×C₄	—	11	1	no	—
63	C₈	—	11	1	no	—
64	C₈	D₄×D₁₁	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	11	1	no	—
67	C₂²	—	88	2	no	—
68	C₂²	—	176	4	no	—
69	C₄	—	11	1	no	—
70	C₄	D₈×D₁₁	1	1	yes	characteristic
71	C₂	—	11	2	no	—
72	C₂	—	16	2	no	—
73	C₂	—	176	2	no	—
74	C₂	D₁₁×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₁×D₁₆
commutator, cosocle	C₁₁×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₁
Fitting	C₁₁×D₃₂	C₂
socle	C₂×C₁₁	C₂×D₁₆
hypercenter	D₃₂	D₁₁
hypocenter	C₁₁	C₂×D₃₂
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₁₁×D₁₆	C₂	semidirect
2. C₁₁×D₃₂	C₂	semidirect
3. #10622157	C₂	semidirect
4. D₃₅₂	C₂	semidirect
5. D₁₁×C₃₂	C₂	semidirect
7. C₁₁×D₁₆	C₂²	semidirect
9. D₁₇₆	C₂²	semidirect
11. C₁₁×C₃₂	C₂²	semidirect
12. C₁₁⋊C₃₂	C₂²	semidirect
31. D₃₂	D₁₁	direct (N × H)
42. D₁₆	C₂×D₁₁	semidirect
45. C₃₂	C₂×D₁₁	semidirect
49. D₁₁	D₃₂	direct (N × H)
57. C₁₁	C₂×D₃₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₁×D₁₆	2
C₁₁×D₃₂	2
#10622157	2
D₃₅₂	2
D₁₁×C₃₂	2
C₂×D₃₂	11

Subgroups — D11×D32 #13070912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×D₃₂ #13070912